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VashaNatasha [74]
2 years ago
11

Which expression converts 100 inches per minute to feet per minute ?

Mathematics
2 answers:
My name is Ann [436]2 years ago
8 0

To convert inches per minute to feet per minute, we can use dimensional analysis to help us cancel out the inches:

\frac{100in}{1min}*\frac{1ft}{12in}

Since we are going to cancel out units that are found on both the top and bottom of the fraction bars, we can cancel out units of inches, and thus we are left with feet per minute.

LenKa [72]2 years ago
3 0

Answer:

The expression is \frac{100inches}{1minute}*\frac{0.08333feet}{1inches}

Step-by-step explanation:

1 inch is equal to \frac{1}{12} feet, so:

\frac{1}{12}ft=0.08333 ft

So, if we have 100 inches per minute, to convert it to feet per minute, we have to use the expression:

\frac{100inches}{1minute}*\frac{0.08333feet}{1inch} = 8.333\frac{ft}{minute}

You need to have attention to put the unit that you need that convert on the denominator to operate and obtain your result.

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X^2-8 = x+4 is your answer!
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3 years ago
The mean of a population is 74 and the standard deviation is 15. The shape of the population is unknown. Determine the probabili
Lena [83]

Answer:

a) 0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

b) 0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c) 0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

The mean of a population is 74 and the standard deviation is 15.

This means that \mu = 74, \sigma = 15

Question a:

Sample of 36 means that n = 36, s = \frac{15}{\sqrt{36}} = 2.5

This probability is 1 subtracted by the pvalue of Z when X = 78. So

Z = \frac{X - \mu}{\sigma}

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{78 - 74}{2.5}

Z = 1.6

Z = 1.6 has a pvalue of 0.9452

1 - 0.9452 = 0.0548

0.0548 = 5.48% probability of a random sample of size 36 yielding a sample mean of 78 or more.

Question b:

Sample of 150 means that n = 150, s = \frac{15}{\sqrt{150}} = 1.2247

This probability is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 71. So

X = 77

Z = \frac{X - \mu}{s}

Z = \frac{77 - 74}{1.2274}

Z = 2.45

Z = 2.45 has a pvalue of 0.9929

X = 71

Z = \frac{X - \mu}{s}

Z = \frac{71 - 74}{1.2274}

Z = -2.45

Z = -2.45 has a pvalue of 0.0071

0.9929 - 0.0071 = 0.9858

0.9858 = 98.58% probability of a random sample of size 150 yielding a sample mean of between 71 and 77.

c. A random sample of size 219 yielding a sample mean of less than 74.2

Sample size of 219 means that n = 219, s = \frac{15}{\sqrt{219}} = 1.0136

This probability is the pvalue of Z when X = 74.2. So

Z = \frac{X - \mu}{s}

Z = \frac{74.2 - 74}{1.0136}

Z = 0.2

Z = 0.2 has a pvalue of 0.5793

0.5793 = 57.93% probability of a random sample of size 219 yielding a sample mean of less than 74.2

5 0
3 years ago
What is the theoretical probability of rolling all 5 dice on the same number?
Kisachek [45]
The theoretical probability of (for example) rolling 5 ones is 1/(6^5) or approximately 0.013%. Because it doesn't matter which number we get five of we can multiply it by 6 to get 1/(6^5) or approximately 0.077%.
4 0
2 years ago
A waitress sold 12 ribeye steak dinners and 39 grilled salmon totaling $575.53 on a particular day. Another day she sold 25 ribe
DedPeter [7]

Answer:

The cost of a ribeye steak dinner is $18.60.

The cost of a grilled salmon dinner is $9.03.

Step-by-step explanation:

let r be the cost of a ribeye steak dinner

let g be the cost of a grilled salmon dinner

Represent the two situations using equations:

12r + 39g = 575.53   (equation 1)

25r + 13g = 582.43   (equation 2)

The best method to use for this case is elimination, which is when you get rid of one of the variables by subtracting or adding.

Since the coefficients for "g" are 39 and 13, they can be eliminated if equation 2 was triple itself.

(25r + 13g = 582.43)  X 3

= 75r + 39g = 1747.29  (new equation 2)

Subtract "equation 1" from "new equation 2"

.   75r + 39g = 1747.29

<u>-   12r + 39g = 575.53</u>

.    63r + 0g = 1171.76    <=we only deal with "r" because 0g is nothing

.             63r = 1171.76    <=divide both sides by 63 to isolate r

.                 r = 18.60       <=rounded from 18.599...

The cost of a ribeye steak dinner is $18.60.

Use any one of the equations to solve for "g", the cost of grilled salmon dinners. I will use equation 1.

12r + 39g = 575.53

Substitute r = 18.6

12(18.6) + 39g = 575.53   <=only one variable now

223.2 + 39g = 575.53     <=subtract 223.2 from both sides

39g = 352.33             <=divide both sides by 39 to isolate g

g = 9.03  <=rounded from 9.0341...

The cost of a grilled salmon dinner is $9.03.

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2 years ago
I need this fast! 30 points!
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